How do you convert (theta) = pi/3(θ)=π3 into cartesian form?

1 Answer
sente
Nov 28, 2015

y = sqrt(3)xy=√3x

Explanation:

There are several equalities used to convert between rectangular and polar coordinates. For a list and good explanation as to why they work, see How do you convert rectangular coordinates to polar coordinates?

In this case, as we have no rr to consider, we will only need

y/x = tan(theta)yx=tan(θ)

Multiplying both sides by xx gives

y = tan(theta)xy=tan(θ)x

But substituting theta = pi/3θ=π3 we get

y = tan(pi/3)xy=tan(π3)x

=> y = sqrt(3)x⇒y=√3x

(Note that this is as expected, as the polar plot theta = pi/3θ=π3 takes on all rr values for the angle pi/3π3, forming a straight line)

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